May, Might, Modality

The expert steps in, and gives an assessment of the situation:

“They might have survived”, they explain.

Now tell me, with what little context you have, how do you read (1)? Did they die? Could they still be out there? Was there something we could have done to save them?

If you assumed they died, you are a pessimist, and likely a drain on the people around you. If you assumed they lived, you’re wrong — they were all eaten alive by lions.

Today’s very short post is about the semantics of modality. Really though, it’s just an excuse for me to share some amusing sentences, focused around usage of the English words may and might; two words, I would venture, that the average native English speaker has trouble defining, and, in fact, whose meanings appear to be changing in modern English. ¹

Modality

First, what exactly was the ambiguity in (1)?

“They might have survived if the lions hadn’t found them.”
“They might have survived — we haven’t found any bodies.”

In (2), it is clear that our heros met an unsavory end. However, (3) is markedly more positive, expressing uncertainty about their fate. In both cases, though, the expert did not say they necessarily survived. So then, how do we model these logically?

To answer that, we need to understand logical modality. I’ve actually written about modality before, but let’s recap.

There are things in this world that are true, like “stop signs are red”. There are also things, however, that could be true, like “stop signs could be blue”.² There are even things that must be true, like “stop signs must have been invented by someone”.³ ⁴

In English, sentences with words like shall, should, can, could, may, might, would, or must (as well as some other words and constructs) express modality. In the simplest case, modality is logically represented with two operators:

Necessity: \(\square P\): \(P\) must be true.
i.e. \(\square \text{SURVIVE}(\text{they})\) could model “they must have survived”.
Possibility: \(\lozenge P\): \(P\) is possibly true.
i.e. \(\lozenge \text{SURVIVE}(\text{they})\) could mode “it is possible they survived”.

Both of these are subtly different than claiming some \(P\) is true. This gets especially tricky with necessity — is there a difference between saying something must be true, and something is true? What’s more, while this is all well and good for (3), it’s not exactly clear how this can be used to model (2). It’s worth us diving into exactly how \(\square\) and \(\lozenge\) work.

Possible Worlds

I need you to do a favor for me, and picture the set of all possible worlds.

That wasn’t so hard, was it?

Let’s call this set \(W\). With this new friend of ours, we can break down our two new operators.

Necessity: \(\square P\): \(\forall w \in W,\; P @ w\)
For all worlds in \(W\), \(P\) is true in that world.
Possibility: \(\lozenge P\): \(\exists w \in W,\; P @ w\)
There exists a world \(w\) in the set of all worlds \(W\), such that \(P\) is true in that world \(w\).

The real magic here is this \(@\) operator, which allows us to express that \(P\) is true in some world. That world might be a world someone believes in (“Li believes she knows the answer”), worlds across time (“it has always been true”), or all logically conceivable worlds (“no matter what, 1 + 1 must be 2!”).

Modality is more than just possibility and necessity; modality allows us to talk about the worlds where propositions are true, and not just the propositions themselves.

Types of Modality

“The set of all worlds” is kinda a tricky idea, of course. In fact, there are a number of various types of modality, each corresponding to a different set of worlds. Here are the most commonly discussed:

Logical Modality

Logical modality deals with the set of all logically consistent worlds, and is one of the strongest / most general modalities.

Possibility	“The first prime can not be 4!”	\(\neg\lozenge_L\)first prime is 4
Necessity	“There must be infinite primes!”	\(\square_L\)there are infinite primes

Epistemic Modality

Epistemic modality deals with a smaller set of worlds — only those worlds consistent with what the speaker knows. This is the “as-far-as-I-know” set. For example, I might know someone has been stealing cookies, based on the state of the cookie jar. It is not logically necessary that someone is stealing cookies, but with the evidence at hand… there must be a cookie-thief among us.

Possibility	“It’s possible he was at the party.”	\(\lozenge_E\)he was at party
Necessity	“The gods must be crazy!”	\(\square_E\)gods are crazy

In “the gods must be crazy”, the meaning here is not that “logically speaking, if there are gods, they must be crazy, in all possible words”. Instead, it’s making a statement about a conclusion the speaker has come to. The speaker has looked around them and said “I don’t know everything about this world, but all signs point towards some bonkers gods”.

Deontic Modality

Deontic modality is substantially different than the others⁵. The set of worlds being described here are the worlds which are being declared “allowed”. I think an example could show this best:

Possibility	“You may have one more slice”	\(\lozenge_D\)you have one more slice
Necessity	“you must come home”	\(\square_D\)you come home

In this case, the speaker isn’t so much declaring conclusions about worlds, but giving commands of a sort.

Might and May

Writing a little intro on modality, however, was really only an excuse to get to a set of sentences I found to be mildly interesting. They come down to this question: what is the difference between “may” and “might”?

At first glance, they are almost interchangeable (both express \(\lozenge\), modal possibility). On closer observation, however, each word is used with a different set of modes.

Mode Type	May	Might
Logical Possibility	Not Used	Used
Epistemic Possibility	Used	Used
Deontic Possibility	Used	Not Used⁶

Now you shouldn’t just take my word for that. Instead, read these example sentences taken from Kearns (2011, 81), and see if you agree with the judgments.

Logical Possibility

She might have fallen down the cliff — thank goodness the safety harness held.
#She may have fallen down the cliff — thank goodness the safety harness held.

Epistemic Possibility

She may have fallen down the cliff — we’re still waiting for the rescue team’s report.
She might have fallen down the cliff — we’re still waiting for the rescue team’s report.

Interesting, no? Kearns (2011) claims that this difference seems to be disappearing in modern English. I haven’t been able to find research supporting that claim, but I’ve been thinking about how I might test it. If I find the time, I’d be interested in doing a little follow up work.

If these judgments don’t line up with your own, I’d love to hear more from you! Or if you could point me to some research on this possible semantic drift in English, that would be just as helpful!

Thanks as always for reading (especially this less-polished post)! Feel free to leave a comment — it always means a lot!

References

Austin, John L., and James O. Urmson. 2009. How to Do Things with Words: The William James Lectures Delivered at Harvard University in 1955. 2. ed., [repr.]. Cambridge, Mass: Harvard Univ. Press.

Kearns, Kate. 2011. Semantics. 2. ed. Modern Linguistics Series. Basingstoke: Palgrave Macmillan.

Of course, modality is a very large topic. This is just a brief introduction. A good, more thorough introduction would be Kearns (2011, chap. 5).↩︎
Like in Hawaii ↩︎
Whoever it was, they were someone in Detroit circa, 1915.↩︎
Note how this is subtly different than “stop signs were invented by someone”.↩︎
One reason why deontic is significantly different than the others is because it has a different “intent” behind it. One uses it with the intention of eliciting a behavior from others. The categorization of a “speech act” is known as illocutionary force. Speech acts are a pretty fascinating topic that should probably be looked into more often in semantics (Austin and Urmson 2009).↩︎
Usage of a deontic “might” does exist, but it’s a bit archaic. “Might I have another?” is typically judged to be correct, but with a feeling of over-formality or datedness. Getting data on these subtle differences strikes me as quite the challenge!↩︎